Construction Of Wave Function Based On Group Method Of Symmetry Scattering Structure

The electromagnetic scattering research has nearly50years of history, along with the development of computer speed and capacity, more and more numerical method is applied to the calculation of the electromagnetic scattering research, in the study we also has many problems need to be solved. The traditional method to seek base function is through the method of variable separation to solve the wave equation, this kind of method is only appropriate for a few regulation boundary conditions theory analysis and application. It is helpless for most low degree symmetrical or complex symmetry boundary problem. So looking for a new method to solve basis functions and applying to the scattering theory and numerical calculation are of great significance to the research. Method of moment is a kind of effective numerical method to solve the electromagnetic boundary problem. How to select the suitable basis functions as better as we can is an important topic to accelerate calculation for method of moment.Group and its representation theory, as a branch of mathematics, is a powerful tool to deal with the physical system with certain symmetry, have widely application in physics, chemistry, and many other areas. Using group method, we can understand the properties directly. It also can simplify the complex calculation. One of the uses is according to the symmetry to look for group well-posed basis functions.Based on the above mentioned theory research, according to the scattering body of the geometry of the symmetrical structure, through the group system research, looking for the given boundary conditions for the base function and using it in method of moment is the main work. In this papers we do much theoretical analysis to method of moment and group method, and choose an example which have certain characteristics of symmetrical two-dimensional physical boundary (three square column), then give detailed theory: first of all, C3v group established by the symmetrical characteristic can set up a multiplication tables, the elements of this multiplication table can be divided into three classes, and then there are three irreducible representation. Second, we can got characteristic mark forms by orthogonality characteristics, write out the C3v group irreducible representation by characteristics mark table and coordinate system transform characteristic, and then find out the symmetrical characteristics base functions, this functions is fit for the requirements of the selection function. Last, The C3v group of tectonic basis functions should use in the method of moment, and prove it has a faster convergence rate. Through the C3v group of examples, this paper also useful for other group to find base function. In complex symmetry structure scattering, we also can use this method to structure function and solution.Group method in electromagnetic field is the basic theory research, the article we show valuable preliminary research in this aspect. Based on the selection of group basis function, we can calculate the electromagnetic scattered radiation field by two-dimensional cylinder scattering integral equation. According to the calculation results, we find out some characters of the base function in solving the scattering problems. Then through these studies, we can make full use of the symmetry characters of group basis function to solve electromagnetic symmetry problem.